To determine the ratio of men to women in the factory, follow these steps:
1. Identify the number of men and women:
- Number of men = 135
- Number of women = 270
2. Form the ratio of men to women:
- The ratio of men to women can be written as [tex]\(\frac{\text{men}}{\text{women}} = \frac{135}{270}\)[/tex].
3. Simplify the fraction:
- To simplify the fraction [tex]\(\frac{135}{270}\)[/tex], find the greatest common divisor (GCD) of both the numerator (135) and the denominator (270).
- The GCD of 135 and 270 can be found by prime factorization or by using the Euclidean algorithm.
4. Finding the GCD using prime factorization:
- Factorize 135: [tex]\(135 = 3 \times 3 \times 3 \times 5 = 3^3 \times 5\)[/tex]
- Factorize 270: [tex]\(270 = 2 \times 3 \times 3 \times 3 \times 5 = 2 \times 3^3 \times 5\)[/tex]
- The common factors are [tex]\(3^3\)[/tex] and [tex]\(5\)[/tex], so the GCD is [tex]\(3^3 \times 5 = 27 \times 5 = 135\)[/tex].
5. Divide both the numerator and the denominator by their GCD:
- [tex]\(\frac{135 \div 135}{270 \div 135} = \frac{1}{2}\)[/tex]
6. Conclusion:
- The simplified ratio of men to women is [tex]\(1:2\)[/tex].
Answer:
The ratio of men to women in the factory is [tex]\(1:2\)[/tex].
